Conebeam CTmicroCT scanners are under rapid development for major biomedical applications. Halfscan

1
Grangeat-Type Half-Scan Algorithms for Cone-Beam
CT
Seung Wook Lee and Ge Wang University of Iowa,
Iowa City, USA http//ct.radiology.uiowa.edu/
CT/Micro-CT Lab
Overview
Circular Half-Scan
Helical Half-Scan
Simulation Results
Cone-beam CT/micro-CT scanners are under rapid
development for major biomedical applications.
Half-scan cone-beam image reconstruction
algorithms only assume data from part of a
scanning turn, and are advantageous in temporal
resolution. While the existing half-scan
cone-beam algorithms are in the Feldkamp
framework, we formulate half-scan algorithms in
the Grangeat framework for the circular and
helical scan cases respectively, and validate
them numerically.
Circular
Grangeat Formula
Helical
Radon value at
Integration plane
Original
Feldkamp half-scan
Grangeat half-scan
Conclusion Future Work
Half-Scan Formula Up to two redundant data
Half-Scan Formula Up to three redundant data
Our Grangeat-type half-scan algorithms minimize
redundant data, optimize temporal resolution, and
outperform Feldkamp-type reconstruction in terms
of image artifacts. Our algorithms are valuable
for quantitative and dynamic biomedical
studies. The following table puts our work in
perspective
Object
Projected Trajectory on Meridian Plane
3D Radon Transform Plane integration normal to
through
Boundary Equation
Inversion Formula Two stage parallel
backprojection
Group 3
Projected trajectory

• Our results differ from the independent work by
  Noo and Heuscher
• We fill data in the Radon space instead of the
  projection domain,
• We consider not only circular but also helical
  scans.
• The future work includes
• Comparison with the method by Noo and Heuscher,
• Extension to the long object case,
• Development of optimal data filling strategies,
• Applications in real biomedical applications.

Region Maps at Four Meridian Angles
(a)
Group 2
Detector plane
Meridian plane
Group 1
References
Double
Single
Shadow (to be interpolated)
Singly Sampled Region
1 G. Wang, C. R. Crawford, and W. A. Kalender,
"Multirow detector and cone-beam spiral/helical
CT," IEEE Trans. Med. Imaging 19, pp. 817-821,
2000 2 G. Wang, Y. Liu, T. H. Lin, and P. C.
Cheng, "Half-scan cone-beam x-ray microtomography
formula," Scanning 16, pp. 216-220, 1994 3 P.
Grangeat, "Mathematical framework of cone beam 3D
reconstruction via the first derivative of the
Radon transform", Mathematical Methods in
Tomography, Lecture notes in Mathematics, eds. G.
T. Herman, A. K. Louis, and F. Natterer, 1497,
pp. 66-97, Springer, Berlin, 1991 4 F. Noo and
D.J. Heuscher, "Image reconstruction from
cone-beam data on a circular short-scan", SPIE
Medical Imaging, San Diego, CA, 2002 5 S. W.
Lee, G. Cho, and G. Wang, "Artifacts associated
with implementation of the Grangeat formula,"
Med. Phys. 29, pp. 2871-2880, 2002 6 S. W. Lee
and G. Wang, "A Grangeat-type half-scan algorithm
for cone-beam CT," Med. Phys. (accepted in 2002,
in press) 7 S. W. Lee and G. Wang,
"Grangeat-type helical half-scan CT algorithm for
reconstruction of a short object ," Med. Phys.
(submitted in 2002, pending) 8 S. W. Lee and G.
Wang, "Grangeat-type half-scan algorithm for
cone-beam CT ," SPIE Medical Imaging, San Diego,
CA, 2003 9 S. W. Lee and G. Wang, "
Grangeat-type helical half-scan CT algorithm for
reconstruction of a long object ," IEEE Trans.
Med. Imag. (in preparation)
Smooth Weighting Functions
Doubly Sampled Region
Doubly Sampled Region
Dashed lines represent the planes normal to the
meridian plane. In the Grangeat framework, the
derivative of Radon data is calculated from the
detector planes associated with the dashed lines.
Geometrically, there can be up to three
intersection points in the helical half-scan case.
Weight 1
Boundaries Weighting Functions
Grangeat Formula Link between cone-beam data
and derivative data in the Radon space
Weight 2
Region map
Weight 1
Weight 2
Weight 3
0, 1
SPIE Medical Imaging Conference, San Diego,  CA,
 USA, February 15-20, 2003